Stat 214 Test 1 study guide

Procedure for approximating the mean with grouped data

- Step 1: Compute the midpoint of each class. The midpoint of a class is found by taking the average of the lower class limit and the lower limit of the next larger class. For the last class, there is no next larger class, but we use the lower limit that the next larger class would have. - Step 2: For each class, multiply the class midpoint by the class frequency. - Step 3: Add the products Midpoint × Frequency over all classes. - Step 4: Divide the sum obtained in Step 3 by the sum of the frequencies.

Parameter

A number that describes a population

Statistic

A number that describes a sample

Median

A number that splits the data set in half. It's resistant because it is not affected much by extreme values.

Sample of Convenience

A sample that is not drawn by a well-defined random method. - Ex: A researcher asks everyone in a particular barbershop their opinions on world politics.

Simple Random Sample

A simple random sample of size n is a sample chosen by a method in which each collection of n population items is equally likely to make up the sample, just as in a lottery. - Ex: a reality show assigns all qualified applicants a number and uses a random number generator to select the participant list.

Randomized experiment

A study in which the investigator assigns the treatments to the experimental units at random.

Sample

A subset of a population, containing the individuals that are actually observed.

Outlier

A value that is considerably larger or considerably smaller than most of the values in the data set

Double-blind experiment

An experiment is double-blind if neither the investigators nor the subjects know who has been assigned to which treatment.

Randomized block experiment

In a randomized block experiment, the subjects are divided into blocks in such a way that the subjects in each block are the same or similar with regard to a variable that is related to the outcome.

Cluster Sampling

Items are drawn from the population in groups or clusters. Ex: Five placement exam testing locations were selected at random and all students at those locations were asked their opinion about the new calculator guidelines.

Nonresponse bias

Occurs when a certain proportion of people who are asked to participate refuse to do so. In many cases, the opinions of nonresponders tend to differ from the opinions of those who do respond. - Ex: a math department chair wants to determine the effectiveness of online homework systems. She emails a questionnaire to 300 college algebra students. 70% of students who returned the survey said that the online homework was helpful. 20 students returned the questionnaire.

Voluntary response bias

Occurs when people are invited to express their opinions on an issue, and the opinions of the people who choose to participate in such surveys do not reflect those of the population as a whole. - Ex: a legendary 80's band is making a best-of-the-best CD compilation. The band publishes a poll on their website for fans to vote on their favorite 30 songs to be included. Over 8,000 people respond. - Voluntary response surveys are highly unreliable in part because people who have strong opinions are more likely to participate.

Social acceptability bias

Occurs when people are reluctant to admit to behavior that may reflect negatively on them. - Ex: a prison ward selects 40 prisoners systematically and asks their opinion on the new rules in the yard and 39 are in favor for the new rules.

Self-interest bias

Occurs when people who have an interest in the outcome of an experiment have an incentive to use biased methods. - Ex: a protein supplement is claimed by its company to yield 15-20% muscle growth in six weeks.

Leading question bias

Occurs when questions are worded in a way that suggests a particular response. - Ex: a political group that supports lowering taxes sent out a survey that included the following question: "Do you favor decreasing the heavy tax burden on middle-class families?" The words "heavy" and "burden" suggest that taxes are too high, and encourage a "Yes" response

Sampling bias

Occurs when some members of the population are more likely to be included in the sample than others. - Samples of convenience almost always have sampling bias, because people who are easy to sample are more likely to be included. It is almost impossible to avoid sampling bias completely, but modern survey organizations work hard to keep it at a minimum.

Voluntary Response Sample

One in which people are invited to lo onto a website, send a text message, or call a phone number, in order to express their opinion on an issue. - Ex: an ad is placed in a newspaper inviting computer owners to call a number to give their opinion about high-speed internet rates.

Observational Study

One in which the assignment to treatment groups is not made by the investigator.

Ordinal variables

Qualitative variables whose categories have a natural ordering

Nominal variables

Qualitative variables whose categories have no natural ordering

Continuous variables

Quantitative variables that can take on any value in some interval. The possible values of a continuous variable are not restricted to any list.

Discrete variables

Quantitative variables whose possible values can be listed. The list may be infinite — for example, the list of all whole numbers.

Quantitative variables

Tell how much or how many of something there is. Data ex: Histogram, Stem-and-lead plots, Dotplots, Time-series plots

Stratified Sampling

The population is divided up into groups, called strata, where the members of each stratum are similar in some way. The a simple random sample is drawn from each stratum. - Ex: A researcher asked a simple random sample of 20 home-schooled children, a simple random sample of 20 children who attend private school, and a simple random sample of 20 children who attend public school their opinion on the new town curfew.

Systematic Sampling

The population items are ordered and every kth item is chosen to include in the sample. - Ex: a caterer is competing for a company's business. The caterer selects every 3rd item off the menu for a tasting.

Treatments

The procedures applied to each experimental unit. There are always two or more treatments. The purpose is to determine whether the choice of treatment affects the outcome.

Outcome/Response

What is measured on each experimental unit.

Subjects

When the experimental units are people, they are sometimes called subjects.

range

largest value - smallest value

coefficient of variance formula

standard deviation divided by mean

upper outlier boundary formula

third quartile + 1.5(interquartile range)

interquartile range formula

third quartile - first quartile

Mean

Calculated by summing all data values and dividing by how many there are.

Qualitative variables

Classify individuals into categories. Data ex: bar graphs, pareto charts, horizontal bars, pie charts

Bias

The degree to which a procedure systematically overestimates or underestimates a population value. - A study conducted by a procedure that tends to overestimate or underestimate a population value is said to be biased. - A study conducted by a procedure that produces the correct result on the average is said to be unbiased.

Population

The entire collection of individuals about which information is sought.

Experimental Units

The individuals that are studied. These can be people, animals, plants, or things.

Statistics

The study of procedures for collecting, describing, and drawing conclusions from information.

Mode

The value in the data set that appears most frequently.